Question 15 Marks
In Fig. $A B \| C D$ and $A C \| B D$. Find the values of $x, y, z$.
Answer
View full question & answer→(i) $x=115^{\circ}, y=65^{\circ}, z=115^{\circ}$"
(ii) $x=40^{\circ}, y=35^{\circ}$
(ii) $x=40^{\circ}, y=35^{\circ}$
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Question 25 Marks
In Fig.$A B \| C D$ and $A E \| C F ; \angle F C G=90^{\circ}$ and $\angle B A C=120^{\circ}$. Find the values of $x, y$ and $z$.
Answer
View full question & answer→$x=60^{\circ}, y=30^{\circ}, z=150^{\circ}$
Question 35 Marks
In Fig. $P Q \| R S$. Find the value of $x$.
Answer
View full question & answer→$75^{\circ}$
Question 45 Marks
In Fig.side $B C$ of $\triangle A B C$ has been produced to $D$ and $C E \| B A$. If $\angle A B C=65^{\circ}$, $\angle B A C=55^{\circ}$, find $\angle A C E, \angle E C D$ and $\angle A C D$.
Answer
View full question & answer→$\angle A C E=55^{\circ}, \angle E C D=65^{\circ}, \angle A C D=120^{\circ}$
Question 55 Marks
In Fig.we have
(i)$\angle M L Y=2 \angle L M Q$, find $\angle L M Q$.
(ii) $\angle X L M=(2 x-10)^{\circ}$ and $\angle L M Q=x+30^{\circ}$, find $x$.
(iii) $\angle X L M=\angle P M L$, find $\angle A L Y$
(iv) $\angle A L Y=(2 x-15)^{\circ}, \angle L M Q=(x+40)^{\circ}$, find $x$
(i)$\angle M L Y=2 \angle L M Q$, find $\angle L M Q$.
(ii) $\angle X L M=(2 x-10)^{\circ}$ and $\angle L M Q=x+30^{\circ}$, find $x$.
(iii) $\angle X L M=\angle P M L$, find $\angle A L Y$
(iv) $\angle A L Y=(2 x-15)^{\circ}, \angle L M Q=(x+40)^{\circ}$, find $x$
Answer
View full question & answer→(i) $60^{\circ}$
(ii) $40^{\circ}$
(iii) $90^{\circ}$
(iv) $55^{\circ}$
(ii) $40^{\circ}$
(iii) $90^{\circ}$
(iv) $55^{\circ}$
Question 65 Marks
In $12.76, A B \| C D$. Find the values of $x, y, z$.
Answer
View full question & answer→$x=55^{\circ}, y=125^{\circ}, z=125^{\circ}$
Question 75 Marks
In Fig. $A B \| C D$ and $\angle 1$ and $\angle 2$ are in the ratio 3: 2. Determine all angles from 1 to 8.
Answer
View full question & answer→$\angle 1=108^{\circ}, \angle 2=72^{\circ}, \angle 3=108^{\circ}, \angle 4=72^{\circ}, \angle 5=108^{\circ}, \angle 6=72^{\circ}, \angle 7=108^{\circ}, \angle 8=72^{\circ}$
Question 85 Marks
In Fig. line $l \| m, \angle 1=120^{\circ}$ and $\angle 2=100^{\circ}$, find out $\angle 3$ and $\angle 4$.
Answer
View full question & answer→$\angle 3=80^{\circ}, \angle 4=40^{\circ}$
Question 95 Marks
In Fig. $A B \| C D$ and a transversal $P Q$ cuts them at $L$ and $M$ respectively. If $\angle Q M D=100^{\circ}$, find all other angles.
Answer
View full question & answer→$\angle P L B=80^{\circ}, \angle P L A=100^{\circ}, \angle A L M=80^{\circ}, \angle B L M=100^{\circ}, \angle L M D=80^{\circ}, \angle L M C=100^{\circ}, \angle C M Q=80^{\circ}$
Question 105 Marks
In Fig. line $l \| m$ and a transversal $n$ cuts them at $P$ and $Q$ respectively. If $\angle 1=75^{\circ}$, find al other angles.
Answer
View full question & answer→$\angle 2=105^{\circ} ; \angle 3=75^{\circ}, \angle 4=105^{\circ}, \angle 5=75^{\circ}, \angle 6=105^{\circ}, \angle 7=75^{\circ}$ and $\angle 8=105^{\circ}$
Question 115 Marks
The line $n$ is transversal to line $l$ and $m$ in Fig. Identify the angle alternate to $\angle 13$, angle corresponding to $\angle 15$, and angle alternate to $\angle 15$.
Answer
View full question & answer→$\angle 7, \angle 7, \angle 5$
Question 125 Marks
In Fig. $A B$ and $C D$ are parallel lines intersected by a transversal $P Q$ at $L$ and $M$ respectively. If $\angle L M D=35^{\circ}$ find $\angle A L M$ and $\angle P L A$.
Answer
View full question & answer→$\angle A L M=35^{\circ}, \angle P L A=145^{\circ}$
Question 135 Marks
In Fig. $A B$ and $C D$ are parallel lines intersected by a transversal $P Q$ at $L$ and $M$ respectively. If $\angle C M Q=60^{\circ}$, find all other angles in the figure.
Answer
View full question & answer→$\angle Q M D=120^{\circ}, \angle P L B=60^{\circ}, \angle A L M=60^{\circ}, \angle M L B=120^{\circ}, \angle D M L=60^{\circ}, \angle C M L=120^{\circ}, \angle A L P=120^{\circ}$
Question 145 Marks
In Fig. find the values of x, y and z.
Answer
View full question & answer→$x=155^{\circ}, y=25^{\circ}, z=155^{\circ}$
Question 155 Marks
In Fig. three coplanar lines intersect at a point $O$, forming angles as shown in the figure. Find the values of $x, y, z$ and $u$.
Answer
View full question & answer→$x=40^{\circ}, y=50^{\circ}, z=90^{\circ}, u=40^{\circ}$
Question 165 Marks
In Fig. lines $l_1$ and $l_2$ intersect at $O$, forming angles as shown in the figure. If $x=45^{\circ}$, find the values of $y, z$ and $u$.
Answer
View full question & answer→$y=135^{\circ}, z=45^{\circ}, u=135^{\circ}$
Question 175 Marks
In Fig.write all pairs of adjacent angles and all the linear pairs.
Answer
View full question & answer→Adjacent angles:
$\angle A O D, \angle C O D ; \angle B O C, \angle C O D ; \angle A O D, \angle B O D ; \angle A O C, \angle B O C$
Linear Pairs: $\angle A O D, \angle B O D ; \angle A O C, \angle B O C$
$\angle A O D, \angle C O D ; \angle B O C, \angle C O D ; \angle A O D, \angle B O D ; \angle A O C, \angle B O C$
Linear Pairs: $\angle A O D, \angle B O D ; \angle A O C, \angle B O C$
Question 185 Marks
In Fig.it thing siven that $\angle=6{ }^{\circ \prime \prime}$, find all other angles.
Answer
View full question & answer→$\angle 2=115^{\circ}, \angle 3=65^{\circ}, \angle 4=115^{\circ}$
Question 195 Marks
In Fig. $O E$ is the bisector of $\angle B O D$. If $\angle 1=70^{\circ}$, find the magnitudes of $\angle 2, \angle 3$ and $\angle 4$.
Answer
View full question & answer→$40^{\circ}, 140^{\circ}, 40^{\circ}$
Question 205 Marks
In Fig.name each linear pair and each pair of vertically opposite angles:
Answer
View full question & answer→Linear pairs:
$\angle 1, \angle 2 ; \angle 2, \angle 3 ; \angle 3, \angle 4 ; \angle 4, \angle 1 ; \angle 5, \angle 6 ; \angle 6, \angle 7 ; \angle 7, \angle 8 ; \angle 8, \angle 5 ; \angle 9, \angle 10$; $\angle 10, \angle 11 ; \angle 11, \angle 12 ; \angle 12, \angle 9$
Pairs of vertically opposite angles:
$\angle 1, \angle 3 ; \angle 2, \angle 4 ; \angle 5, \angle 7 ; \angle 6, \angle 8 ; \angle 9, \angle 11 ; \angle 10, \angle 12$
$\angle 1, \angle 2 ; \angle 2, \angle 3 ; \angle 3, \angle 4 ; \angle 4, \angle 1 ; \angle 5, \angle 6 ; \angle 6, \angle 7 ; \angle 7, \angle 8 ; \angle 8, \angle 5 ; \angle 9, \angle 10$; $\angle 10, \angle 11 ; \angle 11, \angle 12 ; \angle 12, \angle 9$
Pairs of vertically opposite angles:
$\angle 1, \angle 3 ; \angle 2, \angle 4 ; \angle 5, \angle 7 ; \angle 6, \angle 8 ; \angle 9, \angle 11 ; \angle 10, \angle 12$